S4 HOMEWORK 4A
1.
(a)
Simplify
(b)
Factorise fully:
(i)
2.
(i)
50 x 2  18 y 2
3 14
1 
7 15
(ii)
x2  11x  24 (iii)
(ii)
3
2
1 2
5
3
(4)
2 x 2  2 xy  12 y 2
(5)
A Fibonacci sequence is a sequence of numbers.
After the first two terms, each term is the sum of the previous two
terms.
e.g.
13 = 5 + 8
2,
3,
5,
8,
13, . . . . . .
5=2+3
(a)
Write down the next three terms of this Fibonacci sequence.
5,
(b)
-1,
4,
,
,
,
(1)
For the Fibonacci sequence
4,
-3, 1, -2, -1, -3, -4, …………..
(2)
show that the sum of the first six terms is equal to four times
the fifth term.
(c)
If p and q are the first two terms of a Fibonacci sequence,
prove that the sum of the first six terms is equal to four times
(3)
the fifth term.
3
The diagram shows a sector of a circle,
centre W. Find the perimeter of the sector
given that its area is 19.5m2.
(5)
4.
Solve:
(a) 13 − 2𝑛 ≥ 5𝑛 − 8
(b)
2𝑘 − 3(1 − 𝑘) < 2
(5)
25